A succinct, yet thorough definition is provided by Cassio and Rush in the book Green Careers: Choosing Work for a Sustainable Future. They define working in a green career as “working in green jobs that are focused on sustainability and/or environmental protection and preservation. These jobs can be defined by the nature and purpose of the job or by the nature and purpose of the employer.”
The definition for 'Green Career' is vague, but even jobs that wouldn't necessarily fall under the category can be addressed with a 'green' mindset. Approaching careers traditionally lacking a sustainability aspect with a newfound environmentally-conscious or sustainable mindset can be considered 'greening' a career and is an option for all professionals.
U.S. Green Building Council: Green Building Careers
Green America: Getting a Green Job
Let's Go Solar: Green Careers Beyond Solar
The Environmental Career Center
Environmental Science: Sustainability Careers & Green Jobs
Aspen Snowmass: How to Find a Green Job